Question

Given `f(x) = 4x^2 + 9x -4` and `g(x) = -5x^2 + 4x`, what is `(f+g)(x)`?

Answer 1

See a solution process below:

Explanation:

`f(x) + g(x) = (f + g)(x) = (4x^2 + 9x - 4) + (-5x^2 + 4x)`

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

`(f + g)(x) = 4x^2 + 9x - 4 - 5x^2 + 4x`

Next, group like terms:

`(f + g)(x) = 4x^2 - 5x^2 + 9x + 4x - 4`

Now, combine like terms:

`(f + g)(x) = (4 - 5)x^2 + (9 + 4)x - 4`

`(f + g)(x) = -1x^2 + 13x - 4`

`(f + g)(x) = -x^2 + 13x - 4`